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406 CHAPTER 13 Dynamics of a Rigid Body

✔ Checkup 13.2

QUESTION 1: Consider a meterstick falling over, as in Example 2. At what instant is
the angular acceleration produced by the weight force maximum?
QUESTION 2: A rolling cylinder has both rotational kinetic energy (reckoned about
its center of mass) and translational kinetic energy. Which is larger?
QUESTION 3: Consider the rolling cylinder of Example 7. When this cylinder reaches
the bottom of the ramp, is its kinetic energy larger, smaller, or the same as that of a
similar cylinder that slips down a frictionless ramp without rolling?
QUESTION 4: A sphere and a cylinder of equal masses roll down an inclined plane
without slipping. Will they have equal kinetic energies when they reach the bottom?
Which will get to the bottom first?
QUESTION 5: A thin hoop and a solid cylinder roll down an inclined plane without slip-
ping. When they reach the bottom, the translational speed of the hoop is
(A) Less than that of the cylinder
(B) Greater than that of the cylinder
(C) Equal to that of the cylinder

13.3 ANGULAR MOMENTUM
AND ITS CONSERVATION

In Chapter 10 we saw how to express the equation for the translational motion in
terms of the momentum:the rate of change of the momentum equals the force (dp dt
x
F ). Likewise, we can express the equation for rotational motion in terms of angular
x
momentum. The angular momentum of a body rotating about a fixed axis is defined as the
product of the moment of inertia and the angular velocity,

angular momentum L I (13.26)

This equation for angular momentum is analogous to the equation p mv for trans-
2
lational momentum. The SI unit of angular momentum is kg m /s, which can also be
written in the alternative form J s. Table 13.1 gives some examples of typical values
of angular momenta.

According to the data given in Example 4, what is the angular
Concepts EXAMPLE 8
in momentum of the rotor of the Gravity Probe B gyroscope when
Context
spinning at 10000 revolutions per minute?
3
SOLUTION: From Example 4, the angular velocity is 1.05 10 radians/s,
2
and the moment of inertia is
1.1 10 5 kg m .So
3
2
L I
1.1 10 5 kg m 1.05 10 radians/s
2
1.2 10 2 kg m /s